Question

h(t) = -16t² + 8t + k. What is the value of k​

Answer 1

Answer:

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Step-by-step explanation:

Given : (k+2)x

2

−kx+6=0

Putting x=3

(k+2)×9−k×3+6=0

9k+18−3k+6=0

6k=−24

k=−4

Putting k=−4 in given equation

−2x

2

+4x+6=0

x

2

−2x−3=0

x

2

−3x+x−3=0

x(x−3)+1(x−3)=0

(x+1)(x−3)=0

x+1=0 or x−3=0

x=−1 or x=3

Other root of the equation, x=−1

Answer 2

SOLUTION

COMPLETE QUESTION

GIVEN

• Annie was standing on a diving board 48 feet above the water level

• She took a dive into the pool . Her height in feet in water level at any time t sec is given by the polynomial

h(t) = - 16t² + 8t + k

TO DETERMINE

• The value of k.

• The time will she touch the water in the pool

EVALUATION

Here the given polynomial is

h(t) = - 16t² + 8t + k

ANSWER TO QUESTION : 1

By the given condition h(0) = 48

Again h(0) = - 16 × 0² + 8 × 0 + k

⇒ 48 = k

⇒ k = 48

Hence the required value of k = 48

ANSWER TO QUESTION : 2

We have to find the value of t where h(t) = 0

Now the given polynomial is

h(t) = - 16t² + 8t + 48

Now h(t) = 0

⇒- 16t² + 8t + 48 = 0

⇒ 2t² - t - 6 = 0

⇒ 2t² - 4t + 3t - 6 = 0

⇒ ( t - 2 ) ( 2t + 3 ) = 0

t - 2 = 0 gives t = 2

2t + 3 = 0 gives t = - 3/2

Since time can not be negative

So t = 2

Hence the required time = 2 seconds

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